1 // Copyright 2013 The Rust Project Developers. See the COPYRIGHT
2 // file at the top-level directory of this distribution and at
3 // http://rust-lang.org/COPYRIGHT.
5 // Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
6 // http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
7 // <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
8 // option. This file may not be copied, modified, or distributed
9 // except according to those terms.
11 //! Utilities for random number generation
13 //! The key functions are `random()` and `Rng::gen()`. These are polymorphic
14 //! and so can be used to generate any type that implements `Rand`. Type inference
15 //! means that often a simple call to `rand::random()` or `rng.gen()` will
16 //! suffice, but sometimes an annotation is required, e.g. `rand::random::<f64>()`.
18 //! See the `distributions` submodule for sampling random numbers from
19 //! distributions like normal and exponential.
21 //! # Thread-local RNG
23 //! There is built-in support for a RNG associated with each thread stored
24 //! in thread-local storage. This RNG can be accessed via `thread_rng`, or
25 //! used implicitly via `random`. This RNG is normally randomly seeded
26 //! from an operating-system source of randomness, e.g. `/dev/urandom` on
27 //! Unix systems, and will automatically reseed itself from this source
28 //! after generating 32 KiB of random data.
30 //! # Cryptographic security
32 //! An application that requires an entropy source for cryptographic purposes
33 //! must use `OsRng`, which reads randomness from the source that the operating
34 //! system provides (e.g. `/dev/urandom` on Unixes or `CryptGenRandom()` on Windows).
35 //! The other random number generators provided by this module are not suitable
36 //! for such purposes.
38 //! *Note*: many Unix systems provide `/dev/random` as well as `/dev/urandom`.
39 //! This module uses `/dev/urandom` for the following reasons:
41 //! - On Linux, `/dev/random` may block if entropy pool is empty; `/dev/urandom` will not block.
42 //! This does not mean that `/dev/random` provides better output than
43 //! `/dev/urandom`; the kernel internally runs a cryptographically secure pseudorandom
44 //! number generator (CSPRNG) based on entropy pool for random number generation,
45 //! so the "quality" of `/dev/random` is not better than `/dev/urandom` in most cases.
46 //! However, this means that `/dev/urandom` can yield somewhat predictable randomness
47 //! if the entropy pool is very small, such as immediately after first booting.
48 //! Linux 3.17 added the `getrandom(2)` system call which solves the issue: it blocks if entropy
49 //! pool is not initialized yet, but it does not block once initialized.
50 //! `OsRng` tries to use `getrandom(2)` if available, and use `/dev/urandom` fallback if not.
51 //! If an application does not have `getrandom` and likely to be run soon after first booting,
52 //! or on a system with very few entropy sources, one should consider using `/dev/random` via
54 //! - On some systems (e.g. FreeBSD, OpenBSD and Mac OS X) there is no difference
55 //! between the two sources. (Also note that, on some systems e.g. FreeBSD, both `/dev/random`
56 //! and `/dev/urandom` may block once if the CSPRNG has not seeded yet.)
62 //! use std::rand::Rng;
64 //! let mut rng = rand::thread_rng();
65 //! if rng.gen() { // random bool
66 //! println!("int: {}, uint: {}", rng.gen::<int>(), rng.gen::<uint>())
73 //! let tuple = rand::random::<(f64, char)>();
74 //! println!("{}", tuple)
77 //! ## Monte Carlo estimation of π
79 //! For this example, imagine we have a square with sides of length 2 and a unit
80 //! circle, both centered at the origin. Since the area of a unit circle is π,
84 //! (area of unit circle) / (area of square) = π / 4
87 //! So if we sample many points randomly from the square, roughly π / 4 of them
88 //! should be inside the circle.
90 //! We can use the above fact to estimate the value of π: pick many points in the
91 //! square at random, calculate the fraction that fall within the circle, and
92 //! multiply this fraction by 4.
96 //! use std::rand::distributions::{IndependentSample, Range};
99 //! let between = Range::new(-1f64, 1.);
100 //! let mut rng = rand::thread_rng();
102 //! let total = 1_000_000u;
103 //! let mut in_circle = 0u;
105 //! for _ in range(0u, total) {
106 //! let a = between.ind_sample(&mut rng);
107 //! let b = between.ind_sample(&mut rng);
108 //! if a*a + b*b <= 1. {
113 //! // prints something close to 3.14159...
114 //! println!("{}", 4. * (in_circle as f64) / (total as f64));
118 //! ## Monty Hall Problem
120 //! This is a simulation of the [Monty Hall Problem][]:
122 //! > Suppose you're on a game show, and you're given the choice of three doors:
123 //! > Behind one door is a car; behind the others, goats. You pick a door, say No. 1,
124 //! > and the host, who knows what's behind the doors, opens another door, say No. 3,
125 //! > which has a goat. He then says to you, "Do you want to pick door No. 2?"
126 //! > Is it to your advantage to switch your choice?
128 //! The rather unintuitive answer is that you will have a 2/3 chance of winning if
129 //! you switch and a 1/3 chance of winning if you don't, so it's better to switch.
131 //! This program will simulate the game show and with large enough simulation steps
132 //! it will indeed confirm that it is better to switch.
134 //! [Monty Hall Problem]: http://en.wikipedia.org/wiki/Monty_Hall_problem
138 //! use std::rand::Rng;
139 //! use std::rand::distributions::{IndependentSample, Range};
141 //! struct SimulationResult {
146 //! // Run a single simulation of the Monty Hall problem.
147 //! fn simulate<R: Rng>(random_door: &Range<uint>, rng: &mut R) -> SimulationResult {
148 //! let car = random_door.ind_sample(rng);
150 //! // This is our initial choice
151 //! let mut choice = random_door.ind_sample(rng);
153 //! // The game host opens a door
154 //! let open = game_host_open(car, choice, rng);
156 //! // Shall we switch?
157 //! let switch = rng.gen();
159 //! choice = switch_door(choice, open);
162 //! SimulationResult { win: choice == car, switch: switch }
165 //! // Returns the door the game host opens given our choice and knowledge of
166 //! // where the car is. The game host will never open the door with the car.
167 //! fn game_host_open<R: Rng>(car: uint, choice: uint, rng: &mut R) -> uint {
168 //! let choices = free_doors(&[car, choice]);
169 //! rand::sample(rng, choices.into_iter(), 1)[0]
172 //! // Returns the door we switch to, given our current choice and
173 //! // the open door. There will only be one valid door.
174 //! fn switch_door(choice: uint, open: uint) -> uint {
175 //! free_doors(&[choice, open])[0]
178 //! fn free_doors(blocked: &[uint]) -> Vec<uint> {
179 //! range(0u, 3).filter(|x| !blocked.contains(x)).collect()
183 //! // The estimation will be more accurate with more simulations
184 //! let num_simulations = 10000u;
186 //! let mut rng = rand::thread_rng();
187 //! let random_door = Range::new(0u, 3);
189 //! let (mut switch_wins, mut switch_losses) = (0u, 0u);
190 //! let (mut keep_wins, mut keep_losses) = (0u, 0u);
192 //! println!("Running {} simulations...", num_simulations);
193 //! for _ in range(0, num_simulations) {
194 //! let result = simulate(&random_door, &mut rng);
196 //! match (result.win, result.switch) {
197 //! (true, true) => switch_wins += 1,
198 //! (true, false) => keep_wins += 1,
199 //! (false, true) => switch_losses += 1,
200 //! (false, false) => keep_losses += 1,
204 //! let total_switches = switch_wins + switch_losses;
205 //! let total_keeps = keep_wins + keep_losses;
207 //! println!("Switched door {} times with {} wins and {} losses",
208 //! total_switches, switch_wins, switch_losses);
210 //! println!("Kept our choice {} times with {} wins and {} losses",
211 //! total_keeps, keep_wins, keep_losses);
213 //! // With a large number of simulations, the values should converge to
214 //! // 0.667 and 0.333 respectively.
215 //! println!("Estimated chance to win if we switch: {}",
216 //! switch_wins as f32 / total_switches as f32);
217 //! println!("Estimated chance to win if we don't: {}",
218 //! keep_wins as f32 / total_keeps as f32);
227 use iter::{Iterator, IteratorExt};
230 use result::Result::{Ok, Err};
233 #[cfg(not(target_word_size="64"))]
234 use core_rand::IsaacRng as IsaacWordRng;
235 #[cfg(target_word_size="64")]
236 use core_rand::Isaac64Rng as IsaacWordRng;
238 pub use core_rand::{Rand, Rng, SeedableRng, Open01, Closed01};
239 pub use core_rand::{XorShiftRng, IsaacRng, Isaac64Rng, ChaChaRng};
240 pub use core_rand::{distributions, reseeding};
241 pub use rand::os::OsRng;
246 /// The standard RNG. This is designed to be efficient on the current
254 /// Create a randomly seeded instance of `StdRng`.
256 /// This is a very expensive operation as it has to read
257 /// randomness from the operating system and use this in an
258 /// expensive seeding operation. If one is only generating a small
259 /// number of random numbers, or doesn't need the utmost speed for
260 /// generating each number, `thread_rng` and/or `random` may be more
263 /// Reading the randomness from the OS may fail, and any error is
264 /// propagated via the `IoResult` return value.
265 pub fn new() -> IoResult<StdRng> {
266 OsRng::new().map(|mut r| StdRng { rng: r.gen() })
270 impl Rng for StdRng {
272 fn next_u32(&mut self) -> u32 {
277 fn next_u64(&mut self) -> u64 {
282 impl<'a> SeedableRng<&'a [uint]> for StdRng {
283 fn reseed(&mut self, seed: &'a [uint]) {
284 // the internal RNG can just be seeded from the above
286 self.rng.reseed(unsafe {mem::transmute(seed)})
289 fn from_seed(seed: &'a [uint]) -> StdRng {
290 StdRng { rng: SeedableRng::from_seed(unsafe {mem::transmute(seed)}) }
294 /// Create a weak random number generator with a default algorithm and seed.
296 /// It returns the fastest `Rng` algorithm currently available in Rust without
297 /// consideration for cryptography or security. If you require a specifically
298 /// seeded `Rng` for consistency over time you should pick one algorithm and
299 /// create the `Rng` yourself.
301 /// This will read randomness from the operating system to seed the
303 pub fn weak_rng() -> XorShiftRng {
305 Ok(mut r) => r.gen(),
306 Err(e) => panic!("weak_rng: failed to create seeded RNG: {}", e)
310 /// Controls how the thread-local RNG is reseeded.
311 struct ThreadRngReseeder;
313 impl reseeding::Reseeder<StdRng> for ThreadRngReseeder {
314 fn reseed(&mut self, rng: &mut StdRng) {
315 *rng = match StdRng::new() {
317 Err(e) => panic!("could not reseed thread_rng: {}", e)
321 static THREAD_RNG_RESEED_THRESHOLD: uint = 32_768;
322 type ThreadRngInner = reseeding::ReseedingRng<StdRng, ThreadRngReseeder>;
324 /// The thread-local RNG.
325 pub struct ThreadRng {
326 rng: Rc<RefCell<ThreadRngInner>>,
329 /// Retrieve the lazily-initialized thread-local random number
330 /// generator, seeded by the system. Intended to be used in method
331 /// chaining style, e.g. `thread_rng().gen::<int>()`.
333 /// The RNG provided will reseed itself from the operating system
334 /// after generating a certain amount of randomness.
336 /// The internal RNG used is platform and architecture dependent, even
337 /// if the operating system random number generator is rigged to give
338 /// the same sequence always. If absolute consistency is required,
339 /// explicitly select an RNG, e.g. `IsaacRng` or `Isaac64Rng`.
340 pub fn thread_rng() -> ThreadRng {
341 // used to make space in TLS for a random number generator
342 thread_local!(static THREAD_RNG_KEY: Rc<RefCell<ThreadRngInner>> = {
343 let r = match StdRng::new() {
345 Err(e) => panic!("could not initialize thread_rng: {}", e)
347 let rng = reseeding::ReseedingRng::new(r,
348 THREAD_RNG_RESEED_THRESHOLD,
350 Rc::new(RefCell::new(rng))
353 ThreadRng { rng: THREAD_RNG_KEY.with(|t| t.clone()) }
356 impl Rng for ThreadRng {
357 fn next_u32(&mut self) -> u32 {
358 self.rng.borrow_mut().next_u32()
361 fn next_u64(&mut self) -> u64 {
362 self.rng.borrow_mut().next_u64()
366 fn fill_bytes(&mut self, bytes: &mut [u8]) {
367 self.rng.borrow_mut().fill_bytes(bytes)
371 /// Generates a random value using the thread-local random number generator.
373 /// `random()` can generate various types of random things, and so may require
374 /// type hinting to generate the specific type you want.
381 /// let x = rand::random();
382 /// println!("{}", 2u * x);
384 /// let y = rand::random::<f64>();
385 /// println!("{}", y);
387 /// if rand::random() { // generates a boolean
388 /// println!("Better lucky than good!");
392 pub fn random<T: Rand>() -> T {
396 /// Randomly sample up to `amount` elements from an iterator.
401 /// use std::rand::{thread_rng, sample};
403 /// let mut rng = thread_rng();
404 /// let sample = sample(&mut rng, range(1i, 100), 5);
405 /// println!("{}", sample);
407 pub fn sample<T, I: Iterator<Item=T>, R: Rng>(rng: &mut R,
409 amount: uint) -> Vec<T> {
410 let mut reservoir: Vec<T> = iter.by_ref().take(amount).collect();
411 for (i, elem) in iter.enumerate() {
412 let k = rng.gen_range(0, i + 1 + amount);
423 use super::{Rng, thread_rng, random, SeedableRng, StdRng, sample};
426 struct ConstRng { i: u64 }
427 impl Rng for ConstRng {
428 fn next_u32(&mut self) -> u32 { self.i as u32 }
429 fn next_u64(&mut self) -> u64 { self.i }
431 // no fill_bytes on purpose
435 fn test_fill_bytes_default() {
436 let mut r = ConstRng { i: 0x11_22_33_44_55_66_77_88 };
438 // check every remainder mod 8, both in small and big vectors.
439 let lengths = [0, 1, 2, 3, 4, 5, 6, 7,
440 80, 81, 82, 83, 84, 85, 86, 87];
441 for &n in lengths.iter() {
442 let mut v = Vec::from_elem(n, 0u8);
443 r.fill_bytes(v.as_mut_slice());
445 // use this to get nicer error messages.
446 for (i, &byte) in v.iter().enumerate() {
448 panic!("byte {} of {} is zero", i, n)
455 fn test_gen_range() {
456 let mut r = thread_rng();
457 for _ in range(0u, 1000) {
458 let a = r.gen_range(-3i, 42);
459 assert!(a >= -3 && a < 42);
460 assert_eq!(r.gen_range(0i, 1), 0);
461 assert_eq!(r.gen_range(-12i, -11), -12);
464 for _ in range(0u, 1000) {
465 let a = r.gen_range(10i, 42);
466 assert!(a >= 10 && a < 42);
467 assert_eq!(r.gen_range(0i, 1), 0);
468 assert_eq!(r.gen_range(3_000_000u, 3_000_001), 3_000_000);
475 fn test_gen_range_panic_int() {
476 let mut r = thread_rng();
482 fn test_gen_range_panic_uint() {
483 let mut r = thread_rng();
489 let mut r = thread_rng();
490 let a = r.gen::<f64>();
491 let b = r.gen::<f64>();
492 debug!("{}", (a, b));
496 fn test_gen_weighted_bool() {
497 let mut r = thread_rng();
498 assert_eq!(r.gen_weighted_bool(0u), true);
499 assert_eq!(r.gen_weighted_bool(1u), true);
503 fn test_gen_ascii_str() {
504 let mut r = thread_rng();
505 assert_eq!(r.gen_ascii_chars().take(0).count(), 0u);
506 assert_eq!(r.gen_ascii_chars().take(10).count(), 10u);
507 assert_eq!(r.gen_ascii_chars().take(16).count(), 16u);
512 let mut r = thread_rng();
513 assert_eq!(r.gen_iter::<u8>().take(0).count(), 0u);
514 assert_eq!(r.gen_iter::<u8>().take(10).count(), 10u);
515 assert_eq!(r.gen_iter::<f64>().take(16).count(), 16u);
520 let mut r = thread_rng();
521 assert_eq!(r.choose(&[1i, 1, 1]).map(|&x|x), Some(1));
524 assert_eq!(r.choose(v), None);
529 let mut r = thread_rng();
530 let empty: &mut [int] = &mut [];
537 let mut two = [1i, 2];
539 assert!(two == [1, 2] || two == [2, 1]);
541 let mut x = [1i, 1, 1];
543 let b: &[_] = &[1, 1, 1];
548 fn test_thread_rng() {
549 let mut r = thread_rng();
551 let mut v = [1i, 1, 1];
553 let b: &[_] = &[1, 1, 1];
555 assert_eq!(r.gen_range(0u, 1u), 0u);
560 // not sure how to test this aside from just getting some values
561 let _n : uint = random();
562 let _f : f32 = random();
563 let _o : Option<Option<i8>> = random();
567 Option<(u32, (bool,))>),
568 (u8, i8, u16, i16, u32, i32, u64, i64),
569 (f32, (f64, (f64,)))) = random();
577 let mut r = thread_rng();
578 let vals = range(min_val, max_val).collect::<Vec<int>>();
579 let small_sample = sample(&mut r, vals.iter(), 5);
580 let large_sample = sample(&mut r, vals.iter(), vals.len() + 5);
582 assert_eq!(small_sample.len(), 5);
583 assert_eq!(large_sample.len(), vals.len());
585 assert!(small_sample.iter().all(|e| {
586 **e >= min_val && **e <= max_val
591 fn test_std_rng_seeded() {
592 let s = thread_rng().gen_iter::<uint>().take(256).collect::<Vec<uint>>();
593 let mut ra: StdRng = SeedableRng::from_seed(s.as_slice());
594 let mut rb: StdRng = SeedableRng::from_seed(s.as_slice());
595 assert!(order::equals(ra.gen_ascii_chars().take(100),
596 rb.gen_ascii_chars().take(100)));
600 fn test_std_rng_reseed() {
601 let s = thread_rng().gen_iter::<uint>().take(256).collect::<Vec<uint>>();
602 let mut r: StdRng = SeedableRng::from_seed(s.as_slice());
603 let string1 = r.gen_ascii_chars().take(100).collect::<String>();
605 r.reseed(s.as_slice());
607 let string2 = r.gen_ascii_chars().take(100).collect::<String>();
608 assert_eq!(string1, string2);
613 static RAND_BENCH_N: u64 = 100;
620 use self::test::Bencher;
621 use super::{XorShiftRng, StdRng, IsaacRng, Isaac64Rng, Rng, RAND_BENCH_N};
622 use super::{OsRng, weak_rng};
626 fn rand_xorshift(b: &mut Bencher) {
627 let mut rng: XorShiftRng = OsRng::new().unwrap().gen();
629 for _ in range(0, RAND_BENCH_N) {
633 b.bytes = size_of::<uint>() as u64 * RAND_BENCH_N;
637 fn rand_isaac(b: &mut Bencher) {
638 let mut rng: IsaacRng = OsRng::new().unwrap().gen();
640 for _ in range(0, RAND_BENCH_N) {
644 b.bytes = size_of::<uint>() as u64 * RAND_BENCH_N;
648 fn rand_isaac64(b: &mut Bencher) {
649 let mut rng: Isaac64Rng = OsRng::new().unwrap().gen();
651 for _ in range(0, RAND_BENCH_N) {
655 b.bytes = size_of::<uint>() as u64 * RAND_BENCH_N;
659 fn rand_std(b: &mut Bencher) {
660 let mut rng = StdRng::new().unwrap();
662 for _ in range(0, RAND_BENCH_N) {
666 b.bytes = size_of::<uint>() as u64 * RAND_BENCH_N;
670 fn rand_shuffle_100(b: &mut Bencher) {
671 let mut rng = weak_rng();
672 let x : &mut[uint] = &mut [1; 100];